The twisted de Rham cohomology was first studied by Rohm and Witten
[1]} for the antisymmetric field in superstring theory. By
analyzing the massless fermion states in the string sector, Rohm and
Witten obtained the twisted de Rham cochain complex
\((\Omega ^{\ast }(M), d+H_3)\)  for a closed 3-form \(H_3\) , and mentioned
the possible generalization to a sum of odd closed forms. A key
feature in the twisted de Rham cohomology is that the theory is not
integer graded but (like K-theory) is filtered with the grading mod
2. This has a close relation with the twisted K-theory and the
Atiyah-Hirzebruch spectral sequence (see [2]}).
